Question: The grades on a history midterm at Almond are normally distributed with $\mu = 85$ and $\sigma = 2.0$. Michael earned a n $86$ on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Michael's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{86 - {85}}{{2.0}}} $ ${ z \approx 0.50}$ The z-score is $0.50$. In other words, Michael's score was $0.50$ standard deviations above the mean.